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| Math Central | Quandaries & Queries |
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Question from Leanne, a student: A machine makes big widgets. Another machine makes small widgets. 3 small widgets have the same mass as 2 big widgets. It takes the same amount of time to make 3 big widgets as it does to make 5 small widgets. The machines start at the same time and make widgets until the total mass of all the widgets made is equal to the mass of 380 small widgets. What is the total number of widgets made? (Please include workings). |
Hi Leanne,
I can help you get started.
Let's say one time unit is the time required to make 3 big widgets. This is also the time required to make 5 small widgets. Thus in 1 time unit the machines make 3 big plus 5 small widgets. I want to convert this to mass of small widgets but I have 3 big widgets and I know the conversion for 2 big widgets and this is going to give me fractions since 2 doesn't divide 3 evenly. To get around this I want to look at 2 time units.
In 2 time units the machines make 6 big plus 10 small widgets. Now you have 3 pairs of big widgets and each pair has the same mass as 3 small widgets. Hence the 6 big widgets has the mass of 9 small widgets and hence in 2 time units the two machines have produced widgets with a total mass of 9 + 10 = 19 small widgets. How many of these double time units are needed to produce a mass of 380 small widgets? How many widgets of each kind are produced?
I hope this helps,
Penny
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